(x+15)(3x+5)=(5x-7)

Solution for (x+15)(3x+5)=(5x-7) equation:

(x+15)(3x+5)=(5x-7)

We move all terms to the left:

(x+15)(3x+5)-((5x-7))=0

We multiply parentheses ..

(+3x^2+5x+45x+75)-((5x-7))=0


We calculate terms in parentheses: -((5x-7)), so:

(5x-7)

We get rid of parentheses

5x-7

Back to the equation:

-(5x-7)


We get rid of parentheses

3x^2+5x+45x-5x+75+7=0

We add all the numbers together, and all the variables

3x^2+45x+82=0

a = 3; b = 45; c = +82;
Δ = b2-4ac
Δ = 452-4·3·82
Δ = 1041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{1041}}{2*3}=\frac{-45-\sqrt{1041}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1041}}{2*3}=\frac{-45+\sqrt{1041}}{6}
$